But will all of those variants still be considered the "same" sentence? I'm asking because it's popular to make the same claim about Hungarian, but it's not really true. You can switch things around a lot and still get fully grammatical sentences that all relate to the same event. But due to Hungarian's topic/focus structure, the actual meanings expressed by the variants are so different that Hungarian speakers wouldn't consider them "the same sentence expressed a bit differently". Some examples: https://en.wikipedia.org/wiki/Hungarian_grammar#Emphasis
In contrast, I believe Latin is really liberal in its sentence structure, especially in poetry.
There are actually only 7 kinds of सुप्s (x 3 numbers); there are about 10 तिङ्s, but only about 3-4 are in general usage. Then there are other sentence transformations outside these.
The relational modifiers "stick" to the roots, so moving words around the sentence is quite easy - this is particularly useful to poets who need to satisfy certain mathematical rules in their compositions. Much of this is also true for languages like Kannada/Hindi. There was also a paper about a KR scheme inspired by something of this kind.
Sanskrit is generally easy to pick up with the right teachers, in an immersive environment; the grammar-technique, esp. in a "sterile" environment, is rather terrible IMO.